Dinuclear-System (DNS) Model for Fusion and Quasifission Competition — Modeling Nucleon Transfer over the Potential Energy Surface in Heavy Systems

Abstract

The synthesis of superheavy nuclei in heavy-ion fusion reactions is governed by a delicate competition between complete fusion and quasifission, both of which originate from a strongly damped, dissipative configuration of two touching nuclei. The dinuclear-system (DNS) model treats this configuration as a molecule-like complex that evolves by the sequential transfer of nucleons between two well-defined fragments rather than by a monotonic shrinking of the relative distance. This article presents a self-contained formulation of the DNS model in which capture, compound-nucleus formation and survival are computed on a common footing. The nucleus–nucleus interaction potential and the capture barrier are constructed from a Woods–Saxon nuclear term, a point-charge Coulomb term and a rotational term, and capture is evaluated by a Hill–Wheeler transmission. The subsequent evolution of the mass and charge asymmetry is described by a master equation on the potential energy surface, whose driving potential carries the Businaro–Gallone ridge that separates fusion from quasifission. The fusion probability is obtained from the diffusion of the charge distribution across this ridge, while the survival probability against fission is computed from a statistical neutron-versus-fission competition that incorporates shell-corrected fission barriers. The framework is validated against measured evaporation-residue excitation functions for ^48Ca-induced hot-fusion reactions on actinide targets, reproducing both the magnitude and the position of the cross-section maxima within a factor of two to three. The calculations confirm that the steep fall of the fusion probability with increasing charge product is the dominant obstacle to forming the heaviest elements, and they quantify the sensitivity of the predicted residue cross sections to the inner fusion barrier and to the local nuclear temperature